Optimality criterion for a class of nonlinear integer programs

  • Murota K
  • Saito H
  • Weismantel R
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Graver's optimality conditions based on Hilbert bases apply to an integer program with linear equations and a linear objective function. We generalize this result to include a fairly large class of nonlinear objective functions. Our extension provides in particular a link between the superadditivity of the difference-objective function and the Hilbert bases of conic subpartitions of ℝn. © 2003 Elsevier B.V. All rights reserved.

Author-supplied keywords

  • Hilbert bases
  • Integer programming
  • Optimality criterion

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  • Kazuo Murota

  • Hiroo Saito

  • Robert Weismantel

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